split mechanics & leadership
Emily
6/16/2023
This document outlines initial analysis of fission-fusion dynamics using the 1Hz data for Presidente group and Galaxy group.
Contents:
- 1: Frequency of fission and fusion events
- 2: Fission characteristics
- 3: Fusion characteristics
- 4: Leadership analysis
1: Frequency of fission and fusion events:
Manual events were detected based on visually determining when a fission or a fusion occurred by watching videos of the full groups movements for each day. Automated events were detected using an algorithm from Della Libera et al. which has been submitted. These events are only from the 1Hz period.
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2: Fission characteristics
Distance travelled during fissions
Galaxy group
For manual and automated events, we can see that in Galaxy group there tends to be one group moving and one group staying in the same place during fissions. There is also a slight negative correlation with sub-group size and distance travelled, suggesting that smaller subgroups are more likely to move compared to larger subgroups.
Manual events: 
Automated events: 
Presidente group
We see a similar pattern in Presidente group, where one subgroup tends to move and the other subgroup stays in the same place. However, there isn’t a strong relationship between subgroup size and distance travelled.
Manual events: 
Automated events: 
Visualising a fission event
Here, we extract the start and end of the fission event. We classify the group being together when subsequent subgroup centroids were within 15m of each other, and the end of a fission event is when those centroids are 50m apart from one another. These threshold are illustrated as the green lines. The dotted line is where the manual label defined a fission taking place. 
To look at whether specific age/sex classes were more likely to leave, we looked at the proportion of each age/sex class with their distance travelled. We do not see observable differences between age/sex classes:
Galaxy group
Presidente group
3: Fusion characteristics
Distance travelled during fusions
Galaxy group
Similarly to fissions, during fusions events, one subgroup leaves and the other subgroup stays in the same place. For the majority of fission, the initial full group moved less than 30m. There is a slight negative correlation with subgroup size and distance travelled during a fusion.
Manual events: 
Automated events: 
Presidente group
As with Galaxy group, most fissions in Presidente group were caused by one subgroup leaving a stationary subgroup. There is a slight negative correlation is subgroup size and distance travelled during a fission event. The distance travelled of the full group prior to the split was most commonly less than 40m for the manual events and less than 50m for the automated events.
Manual events: 
Automated events: 
Visualising a fusion event
4: Leadership
For this analysis, we wanted to determine which individuals in the group are leaders and followers and are these positions consistent across events. For this, we subsetted the data to subgroups which moved more than 15m. If both subgroups moved, leadership analysis would be done on both of the subgroups seperately. We defined leadership using two methodologies:
- Spatial rank: this is based on their position along the groups movement vector at a particular time, with the individual furthest in the direction of the groups end trajectory being the leader. Group members are ranked along this trajectory from 1 (leader - individual closest to t2) to 0 (last individual along trajectory). The diagram below is the full group at t1 splitting into two subgroups at t2, with the ranks defined as the distance each individual is from the start location (average location of subgroup at t1).
- Crossing rank: This is defining a threshold which group members cross a defined trajectory, and extracting the order of crossing this threshold (ranked the same as method 1), with the first individual crossing over the threshold first being the leader.
The results shown in this document are from the second method, with the order of individuals crossing a threshold defining their leadership score. For these results, we chose the threshold as being 50% of the distance from the start of the fission to the end of the fission (basically halfway between the green lines on the “visualising a fission event” plot). We also ran these analyses on method 1 which gave similar results. We also found there to be no clear differences in the results for manual vs the automated events, except for the quantity of events captured. Therefore, all further results are from the automated events, due to sample size.
Galaxy group
For each fission and fusion event, each individual was assigned as a “mover” if they travelled more than 15m during the event, from this, we calculated the percentage moved for each individual. We can see that Gus (single adult male in the group) moved more during fissions and fusions, however there are no clear differences between group members on which individuals were more likely to leave during a fission event and move towards the group during a fusion event.
Percentage each individual moved for events with 95% Clopper Pearson interval:
Leadership during fissions
This is the frequency distribution of each group member of Galaxy group being a leader (at position 1) to being a follower (at position 0) during a fission event. We can see some variation between group members, but take note that the number of events is low, which may drive inaccurate conclusions on which individuals consistently lead. 
Leadership during fusions
This is the frequency distribution of each group member of Galaxy group being a leader (at position 1) to being a follower (at position 0) during a fusion event. Again, the number events is relatively small. 
Comparing entropy between real and permuted data
To characterize individual consistent in rank position of subgroup members for fissions and fusions, we took the entropy of each individual’s distribution of leadership ranks across all events where they were in the leaving/joining group, then took the mean across individuals as our test statistic. If there was high consistency in rank position (for example, if one individual was consistently the leader), then their entropy value would be low. We compared the groups test statistic with simulated data. Simulated data were the random allocations of each group members rank for each event. If there was consistency in individual position, the groups entropy value (red line) would not be in the distribution of the simulated data. As the red line is within the distribution of the simulated data, these results shows that Galaxy group do not have consistent positions during fission and fusion events.
Presidente group
For each fission and fusion event, each individual was assigned as a “mover” if they travelled more than 15m during the event, from this, we calculated the percentage of time each individual moved. Bear in mind, Wildflower was not in Presidente group, so did not partake in fission or fusion events.
Percentage each individual moved for all events with 95% Clopper Pearson interval:
Leadership during fissions
This is the frequency distribution of each group member of Presidente group being a leader (at position 1) to being a follower (at position 0) during a fission event. 
Leadership during fusions
This is the frequency distribution of each group member of Presidente group being a leader (at position 1) to being a follower (at position 0) during a fusion event. 
Comparing entropy between real and permuted data
As with Galaxy group, Presidente group also show no consistent positions in fission and fusion events. 